Or the "two base theory" as it is known to most of the communnity - i prefer using the term "hypothesis" because that's closer to what it is.
So in short. Is the two-base hypothesis correct? It must be. Everything proven and explained by a single, little statement by Goku, when he described what Super Saiyan Blue is.
"It's what you get when a Saiyan with the power of a Super Saiyan God transforms into Super Saiyan".
This very statement gives you everything you need to know or care about, there's really nothing more to it. Once a Saiyan who has the power of SSj God transforms into SSj, the result is SSj Blue.
So how do you explain Goku and Vegeta showing regular Super Saiyan in later sagas? Well, that's what happens when a Saiyan WITHOUT the power of SSj God transforms into Super Saiyan. Because if one has that power, they will go SSj Blue instead. Inevitably.
Out of universe you can obviously explain this by fanservice and wanting to provide nostalgia fuel. It's a big shame, even more so since Toriyama went back on his word that Goku and Vegeta wouldn't be using the regular SSj forms anymore - and when Blue came into the picture we all knew pretty damn well why. But then they all showed how little balls they had and created this whole current mess, with Goku being able to go up to SSj3 - and bothering to do so even though he can access power leaps and bounds higher without transforming at all, just by tapping into his god power in base form. Too bad the "Saiyan beyond God" state seems to have been retired, possibly because watching transformed characters fight is more attractive to viewers? I really have no idea what they were thinking. Urgh.
So yeah, it goes Base -> SSj -> SSj2 -> SSj3 or God Base -> SSj Blue. Alternatively, you go from regular SSj to SSj Blue by activating God Ki while being a Super Saiyan. Beause yeah, SSj Blue is when a Saiyan with the power of a Super Saiyan God transforms into Super Saiyan. There.